$\begin{array}{l} \text{Gegeben:} \\ a1 \cdot x +b1 \cdot y =c1\\ a2 \cdot x +b2 \cdot y =c2 \\ \\ \text{Gesucht:} \\\text{x und y} \\ \\ \textbf{Gegeben:} \\ \\ -\frac{1}{2}x +4y =6\\ -2x -8y = 2 \\ \\ \\ \\ \textbf{Rechnung:} \\\begin{array}{l|l} \begin{array}{l} I \qquad -\frac{1}{2} x +4 y =6\\ II \qquad -2 x -8 y = 2 \\ \text{I nach x auflösen}\\ -\frac{1}{2} x +4 y =6 \\ -\frac{1}{2} x +4 y =6 \qquad /-4 y\\ -\frac{1}{2} x =6 -4 y \qquad /:\left(-\frac{1}{2}\right) \\ x =-12 +8 y \\ \text{I in II}\\ -2 (-12 +8 y ) + -8 y = 2 \\ 24 -16 y -8 y = 2 \qquad / -24 \\ -16 y -8 y = 2 -24 \\ -24 y = -22 \qquad /:\left(-24\right) \\ y = \frac{-22}{-24} \\ y=\frac{11}{12} \\ x =-12 +8 y \\ x =-12 +8 \cdot \frac{11}{12} \\ x=-4\frac{2}{3} \\ L=\{-4\frac{2}{3}/\frac{11}{12}\} \end{array} & \begin{array}{l} I \qquad -\frac{1}{2} x +4 y =6\\ II \qquad -2 x -8 y = 2 \\ \text{I nach y auflösen}\\ -\frac{1}{2} x +4 y =6 \\ -\frac{1}{2} x +4 y =6 \qquad /+\frac{1}{2} x\\ 4 y =6 +\frac{1}{2}x \qquad /:4 \\ y =1\frac{1}{2} +\frac{1}{8}x \\ \text{I in II}\\ -2x + -8(1\frac{1}{2} +\frac{1}{8} x ) = 2 \\ -12 -1 x -8 x = 2 \qquad / -\left(-12\right) \\ -1 x -8 x = 2 -\left(-12\right) \\ -3 x = 14 \qquad /:\left(-3\right) \\ x = \frac{14}{-3} \\ x=-4\frac{2}{3} \\ y =1\frac{1}{2} +\frac{1}{8} x \\ y =1\frac{1}{2} +\frac{1}{8} \cdot \left(-4\frac{2}{3}\right) \\ y=\frac{11}{12} \\ L=\{-4\frac{2}{3}/\frac{11}{12}\} \end{array} \end{array} \end{array}$